Place beets in a large pot, cover with cold water, and bring to a boil over high heat. Once boiling, reduce heat to medium and simmer until beets are fork tender, about 30 minutes. Drain, then peel under cold running water. Set beets aside to cool.
Trim any green tops off fennel and slice bulbs in half lengthwise. Remove core from each half and slice bulbs lengthwise in 1/4-inch-thick strips.
Return the large pot to the stove, add olive oil and butter, and heat over medium heat. When butter foams, add fennel, season well with salt and freshly ground black pepper, and cook, stirring occasionally, until just tender, about 5 minutes.
Add vermouth, mustard, and lemon juice and bring to a simmer. Meanwhile, slice peeled beets into 1/4-inch-thick rounds. Add beets to the pot and cook until warmed through, about another 5 minutes. Stir in herbs, taste, and adjust seasoning as desired.
Beverage pairing: Château de La Chaize Brouilly, France. Beets can be great with either white or red wine, but the Gamay grape from Beaujolais is particularly adept at matching a beet’s combination of earthy and sweet flavors stride for stride. The wine is dry, but is a lovely combination of soil, grape, and leaf tastes, matched with some punchy tannins and acid to give the whole combination some structure.
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